Since your budget is around 10K, I would be looking at travel trailers, Class A and Class C, all with no slides. You will find loads of bargains. Class B's seem way overpriced. I think you could quickly grow tired of living fulltime in a Class B.
I've been living in a 1994, Class C, 28 footer,30 amp, no slides, for almost 2 years with a ridiculous little dog. I've been to 17 states and put 10,000 miles on it. Due to my own budget considerations, I don't own a car at all, but I don't have a daily commute either. I work at home and often workamp (trade labor for rent & utilities). Class C's are able to tow a car (the prior owners towed a Saturn) with mine.
If you are going to have a commute, I would still say look at Class A and Class C's with no slides, and then drive a junker to commute with if budget is a consideration in both areas. Some folks have to have a top of the line newish cars, others like me are happy with old clunkers. (I've driven several old clunkers with good luck in the past.) I bought an old clunker while I was shopping for an RV, once it was bought, I resold it and amazingly came out even.
I have only 30 amp service and use a 1500 watt ceramic heater in the winter. If it can't keep up, I supplement with the propane furnace. If you are planning to be parked a while, you can have a large propane tank delivered to your lot for using the propane heater, stove and hot water so you don't have to refill the tiny tanks all the time. I also have a tiny 200watt ceramic heater (super handy for foot warming, keeping the bathroom toasty etc, matter of fact, I might get a 2nd one). I use a 180 watt mattress warmer at night on the bed (heaven on earth). I installed a 400watt electric hot water kit which I use year round though I have the propane option. My 200watt crockpot seems to be in use 5-6-7 times a week, all day. Plus I run computer equipment, TV, stereo, 5 medical devices, and assorted rechargers. All this on 30 amp. Oh and I cook in the 1100 watt microwave quite often. My fridge is running on electric too. I sometimes use the A/C fan to stir the hot air around in the winter from the ceramic heater. If you deflect the A/C vents so the air is not blowing directly on you it does do wonders to spread the heat around the motorhome more evenly. The direct air from the AC fan won't feel hot like a forced air furnace, but it will stir the hot air around and make the RV cozier.
I try to maintain my RV nicely, and thus far have not been turned away from any parks or campgrounds due to age alone. But I rarely stay long term in one spot, except when workamping.
I think if you look at travel trailers, Class A and Class C, (all with no slides as you prefer) you will find an abundance under $10,000. Many that are privately up for sale are way overpriced, as time goes on the owners are willing to get more reasonable. So watch those in the $20,000+ range too, give the owners your phone number in case they drop the price weeks, months down the road (many do!). I was very partial to the Class C, because they tend to have a lot less systems to work on than the Class A's. I do some of my own maintenance, upgrades and repairs. I used the Ford dealer for my engine and generator maintenance. I try to avoid RV dealers for work except when forced to (due to their rather high labor costs. )
As for laundry, I bought a compact portable washing machine from Haier that quick connects to my bathroom or kitchen sink and is less than 18 inches square. I do small loads and often hang them up inside to dry overnight. Sometimes I am able to hang stuff up outside to dry much quicker. I put in a compression post and flanges in the shower near the ceiling, then I hang my clothes on hangers to dry. Towels and undies, I simply use clothes pins to hang them from the clothes hangers too while drying. I have a 12volt clip on fan that is super powerful. I can clamp this in the shower to help speed dry the clothes. once that small load is dry, I can wash the next load to hang up.
I am in LOVE with the washing machine, it cleans super well. I don't mind not having a dryer (no room for one) as thus far everything line dries inside or out, just fine.
One other thought, climb up the ladder and look closely at the roof, take lots of pictures too. Staying nice and dry in an RV is just as important as in a boat. Matter of fact, takes loads of pics of any RV that strikes your fancy, so that you can refer back to them, as you mull over whether to make an offer on it or not.
Try to have 1-2k set aside for emergency repairs or upgrades when you buy an older unit, in case you do find a surprise afterwards, but assuming everything is OK, you have some spare change to make some little upgrades should you get comfy and need a few things added or upgraded.
Ebay has lots of older rigs with no slides on auction, but certainly go see the unit in person first, before placing any bids at all, unless you just like to be a big gambler.
I hope some of this info helps!
PS... I do think you are putting too much emphasis on brand names. Look for the things that count, past maintenance by the past owners, is often very critical. Also, some manufacturers had good years and bad years. That just makes it even more confusing.
I am also surprised about the 5 year comment on appliances. I am still using the 1994 stove, microwave, A/C, furnace, hot water and built-in coffee maker. It does look like the prior owner had some major fridge work done, but it has performed flawlessly for me.