Based in your circumstances (Initial deposit £1-2K. I'll assume a median of £1500) followed by £400-500 p.m., I'd recommend:
1) Halifax 4% Help to buy ISA - Initially deposit £1200 to maximise the potential of this account. Then deposit £200 monthly.
2) First Direct Current account - Switch from your current bank to first direct and get £150. This is equivalent to saving £1000 at a 15% rate for a year, so it's a good bonus to have.
One point to make though, to receive the bonus £150, you have to deposit £1000 within the first 3 months of opening the account, which shouldn't be a problem. Just make sure you deposit that initial bonus into the account before opening the halifax account.
3) First Direct Regular Saver - 6% interest - Where you can save up to £300 a month. But you have to be able to save regularly for at least a year. Pros: Forces you to save regularly, high interest, fits your budget as you can vary the amount each month if you want. Cons: You have to save every month.
You can deposit the remaining £300 from your initial bonus here to start you off.
The above scenario allows you split your £500 a month perfectly between a 4% and a 6% rate, and they are both flexible in that you don't have to put in the maximum but the option is there.
The alternative TSB account at 5% is fine too but it is capped at £2000. So if you manage to save £300 a month in that account you'll reach the limit in 7 months. I wouldn't recommend it if you're going to be doing this 'over the next few years'.
Hope this helps.